If you gave +2 to a 4 might unit, does blighted battleaxe still kill it at the end of your turn?

No — the unit survives. The +2 is still active when the Battleaxe trigger fires, so the unit has 6 Might when it takes 4 damage, and 4 damage isn't lethal (damage only kills when it equals or exceeds current Might).

Timing matters here: "at the end of your turn" effects resolve during the Ending Step, but "this turn" effects don't expire until the Expiration Step that follows (Rule 317.2.c). So the 4 damage lands against the boosted 6 Might. And even in a case where the damage did threaten the unit, the Ending Special Cleanup heals all units immediately after, so it wouldn't carry over.

One caveat: if the +2 has a shorter duration than end of turn (e.g., "until end of combat" or a temporary Mighty buff), then the unit would be back at 4 Might when the trigger fires and the 4 damage would be lethal — before cleanup heals it.